Answer:
(-∞, 4)
Explanation:
"The function f(x)= -(x+5)(x+1) is down" should be "The function f(x)= -(x+5)(x+1) has a parabolic graph that opens down."
Expanding f(x)= -(x+5)(x+1), we get f(x) = -[x^2 + 6x + 5] = -x^2 - 6x - 5.
Here the coefficients are a = -1, b = -6 and c = -5. Thus, the axis of symmetry is
-(-6)
x = ------------ = -3.
2(-1)
The maximum value of the function occurs when x = -3.
We must also find the actual max value.
It is f(-3) = -(-3)^2 - 6(-3) - 5, or 4.
The max value is 4. Thus, the range of this function is (-∞, 4)